The optimization process and recommendations:

1. Create Optimal Indexes (modified query below): The recommended indexes are an integral part of this optimization effort and should be created before testing the execution duration of the optimized query.
2. Replace Join With Exists To Avoid Redundant Grouping (modified query below): When a joined table isn’t used anywhere other than in the WHERE clause, it's equivalent to an EXISTS subquery, which often performs better. In cases where the DISTINCT or GROUP BY clause contains only columns from the Primary key, they can be removed to further improve performance, as after this transformation, they are redundant.

Optimal indexes for this query:

ALTER TABLE `table_1` ADD INDEX `table_1_idx_visitor_id` (`visitor_id`);
ALTER TABLE `table_2` ADD INDEX `table_2_idx_visitor_id_company_id_visited_on` (`visitor_id`,`company_id`,`visited_on`);

The optimized query:

SELECT
        t1.visitor_id 
    FROM
        table_1 AS t1 
    WHERE
        (
            1 = 1 
            AND 1 = 1
        ) 
        AND (
            EXISTS (
                SELECT
                    1 
                FROM
                    table_2 AS t2 
                WHERE
                    (
                        (
                            t2.visitor_id = t1.visitor_id
                        ) 
                        AND (
                            t2.company_id IN (
                                528, 211, 1275, 521, 1299, 493, 492, 852, 868, 869, 1235, 486, 485, 1238, 855, 1237, 651, 538, 1241, 1240, 548, 543, 1247, 1253, 490, 468, 582, 583, 569, 477, 488, 802, 1294, 518, 1274, 476, 545, 1267, 556, 479, 1266, 1265, 541, 1189, 1263, 1152, 1260, 478, 1257, 885, 1139, 1256, 804, 708, 547, 561, 1239, 1142, 1226, 1148, 1230, 529, 1223, 1192, 1191, 874, 830, 822, 818, 817, 794, 718, 487, 709, 706, 705, 669, 513, 455
                            )
                        )
                    ) 
                    AND (
                        t2.visited_on BETWEEN '2015-01-01' AND '2017-01-31'
                    )
            )
        ) 
    GROUP BY
        t1.visitor_id 
    ORDER BY
        t1.`visits_count` DESC LIMIT 20